Constantin P. Niculescu, Holger Stephan: Lagrange's Barycentric Identity From An Analytic Viewpoint, p.487-496

Abstract:

A probabilistic extension of Lagrange's barycentric identity is proved and used to provide new insights into the mechanism of Jensen's inequality. In particular, it is shown that every instance of Jensen's inequality comes from an identity.

Key Words: Jensen's inequality, Lagrange's algebraic identity, convex function, barycenter of a measure.

2000 Mathematics Subject Classification: Primary: 26B25;
Secondary: 26D15.

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